Cremona's table of elliptic curves

12716 = 2² · 11 · 17²

Field	Data	Notes
Atkin-Lehner	2- 11- 17+	Signs for the Atkin-Lehner involutions
Class	12716c	Isogeny class
Conductor	12716	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	1512	Modular degree for the optimal curve
Δ	-813824 = -1 · 28 · 11 · 172	Discriminant
Eigenvalues	2-  0  3  2 11- -2 17+  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-136,612]	[a1,a2,a3,a4,a6]
Generators	[8:6:1]	Generators of the group modulo torsion
j	-3760128/11	j-invariant
L	5.8753734300267	L(r)(E,1)/r!
Ω	2.8351290866627	Real period
R	0.69078258877949	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	50864bb1 114444h1 12716b1	Quadratic twists by: -4 -3 17

Hecke Eigenvalues for elliptic curve 12716c1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	0	3	2	-	-2	+	2	-3	-8	-1	-2	2	-4	-9	2	4	-6	3	1	-8	-4	0	-9	-13

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Quadratic twists for elliptic curve 12716c1

-4	-3	17
50864bb1	114444h1	12716b1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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